Coding Theory and Bilinear Complexity PDF Download
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Author: Salahoddin Shokranian
Publisher:
ISBN:
Category : Coding theory
Languages : en
Pages : 422
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Book Description
Author: Salahoddin Shokranian
Publisher:
ISBN:
Category : Coding theory
Languages : en
Pages : 422
Get Book Here
Book Description
Author: Igor Shparlinski
Publisher: Springer Science & Business Media
ISBN: 940159239X
Category : Mathematics
Languages : en
Pages : 532
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Book Description
This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.
Author: Peter Bürgisser
Publisher: Springer Science & Business Media
ISBN: 3662033380
Category : Mathematics
Languages : en
Pages : 630
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Book Description
The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
Author: Alp Bassa
Publisher: American Mathematical Soc.
ISBN: 1470428105
Category : Computers
Languages : en
Pages : 210
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Book Description
This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18–22, 2015. Since the first meeting almost 30 years ago, the biennial AGCT meetings have been one of the main events bringing together researchers interested in explicit aspects of arithmetic geometry and applications to coding theory and cryptography. This volume contains original research articles reflecting recent developments in the field.
Author: W. Cary Huffman
Publisher: CRC Press
ISBN: 1351375105
Category : Computers
Languages : en
Pages : 998
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Book Description
Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research
Author: Samuele Anni
Publisher: American Mathematical Society
ISBN: 1470467941
Category : Mathematics
Languages : en
Pages : 198
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Book Description
This volume contains the proceedings of the 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, held (online) from May 31 to June 4, 2021. For over thirty years, the biennial international conference AGC$^2$T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers together to forge connections between arithmetic geometry and its applications to coding theory and to cryptography. The papers illustrate the fruitful interaction between abstract theory and explicit computations, covering a large range of topics, including Belyi maps, Galois representations attached to elliptic curves, reconstruction of curves from their Jacobians, isogeny graphs of abelian varieties, hypergeometric equations, and Drinfeld modules.
Author: David Joyner
Publisher: Springer Science & Business Media
ISBN: 3642596630
Category : Mathematics
Languages : en
Pages : 264
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Book Description
These are the proceedings of the Conference on Coding Theory, Cryptography, and Number Theory held at the U. S. Naval Academy during October 25-26, 1998. This book concerns elementary and advanced aspects of coding theory and cryptography. The coding theory contributions deal mostly with algebraic coding theory. Some of these papers are expository, whereas others are the result of original research. The emphasis is on geometric Goppa codes (Shokrollahi, Shokranian-Joyner), but there is also a paper on codes arising from combinatorial constructions (Michael). There are both, historical and mathematical papers on cryptography. Several of the contributions on cryptography describe the work done by the British and their allies during World War II to crack the German and Japanese ciphers (Hamer, Hilton, Tutte, Weierud, Urling). Some mathematical aspects of the Enigma rotor machine (Sherman) and more recent research on quantum cryptography (Lomonoco) are described. There are two papers concerned with the RSA cryptosystem and related number-theoretic issues (Wardlaw, Cosgrave).
Author: Henning Stichtenoth
Publisher: Springer
ISBN: 3540472673
Category : Mathematics
Languages : en
Pages : 235
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Book Description
About ten years ago, V.D. Goppa found a surprising connection between the theory of algebraic curves over a finite field and error-correcting codes. The aim of the meeting "Algebraic Geometry and Coding Theory" was to give a survey on the present state of research in this field and related topics. The proceedings contain research papers on several aspects of the theory, among them: Codes constructed from special curves and from higher-dimensional varieties, Decoding of algebraic geometric codes, Trace codes, Exponen- tial sums, Fast multiplication in finite fields, Asymptotic number of points on algebraic curves, Sphere packings.
Author: Stéphane Ballet
Publisher: American Mathematical Soc.
ISBN: 1470414619
Category : Computers
Languages : en
Pages : 316
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Book Description
This volume contains the proceedings of the 14th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held June 3-7, 2013, at CIRM, Marseille, France. These international conferences, held every two years, have been a major event in the area of algorithmic and applied arithmetic geometry for more than 20 years. This volume contains 13 original research articles covering geometric error correcting codes, and algorithmic and explicit arithmetic geometry of curves and higher dimensional varieties. Tools used in these articles include classical algebraic geometry of curves, varieties and Jacobians, Suslin homology, Monsky-Washnitzer cohomology, and -functions of modular forms.
Author: Harald Niederreiter
Publisher: Princeton University Press
ISBN: 140083130X
Category : Mathematics
Languages : en
Pages : 273
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Book Description
This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books
